The line was crackly, but if Felix Baumgartner was feeling even the slightest bit nervous, as he prepared to step into some exceedingly thin air 128,100 feet above the deserts of New Mexico he did a good job of hiding it.

"The whole world is watching,” the Austrian daredevil declared, in a tone that bordered on nonchalance. “I wish that you could see what I see!” Then, having been assured by Mission Control that some sort of guardian angel would look after him, he flashed a “thumbs up” sign and threw himself into the stratosphere.

It was a giant leap, all right. From a height of roughly 24 miles, Baumgartner spent four minutes and 22 seconds in freefall, hitting a top speed of 833.9mph and therefore achieving his signature objective of becoming the first skydiver to break the speed of sound.

He also broke long-standing records for the highest skydive in history, and the highest balloon flight on record. But the biggest thrill was simply surviving. “When I was standing there on top of the world, you become so humble, you do not think about breaking records anymore, you do not think about gaining scientific data,” he said afterwards. “The only thing you want is to come back alive."

In keeping with tradition, Baumgartner’s giant leap ended with some small steps. Almost 10 minutes after entering into freefall, he quite literally hit the ground running, beneath a red-and-white parachute adorned with the logo of Red Bull, the fizzy drink company which bankrolled the stunt. He jogged for a few yards before coming efficiently to a halt in an empty field.

Live footage, from long-lens television cameras aboard a circling helicopter, showed Baumgartner raise his arms in a victory salute. Then he removed his helmet, revealing a smile so wide that you could see the whites of his teeth. “Sometimes you have to get up really high to know how small you are,” he reflected.

Three hours earlier, the world had begun watched as “Fearless Felix”, to use his officially sanctioned nickname, was strapped into a tiny 8ft by 11ft fibreglass capsule. It dangled beneath a huge helium balloon made from wafer-thin plastic which when fully extended was the height of a 55-storey building.

A total of 30 cameras had been rigged up to record proceedings, from a wide range of vantage points, and the result was rolling television gold: undeniably spectacular, but with a sense of danger that lent genuine drama to proceedings.

Seven million watched on YouTube, while tens of millions more tuned in via regular television, helped by the fact that Red Bull’s PR department scheduled the jump to coincide with European evening primetime. More than half the globally trending topics on Twitter yesterday involved Baumgartner. After he landed, an official picture posted to Facebook generated nearly 216,000 likes, 10,000 comments and more than 29,000 shares in less than 40 minutes.

Despite being billed as live, the leap was in fact shown on a 20-second time delay in case of a tragic accident. But organisers did a good job of keeping the nerves of viewers jangling. As Baumgartner’s balloon took off, the cameras cut to his mother, Ava, who was watching with friends and family. She was crying, nervously.

During the two hours that her 43-year-old son continued on his long upward journey, we learned of many potential ways in which he could meet with a sticky end, for example by accidentally tearing his pressurised suit upon leaving the capsule, which would have apparently cut off his oxygen supply and caused “lethal bubbles” would quickly form in his bodily fluids.

The sense of impending doom rose roughly two thirds of the way through the ascent, when it emerged that a “minor issue” had developed with Baumgartner’s heated face-mask, which was steaming up. Organisers attempted to “trouble-shoot” it, and for a time considered calling the jump off. But eventually they decided to throw caution to the wind.

That decision didn’t always look questionable. A short while into the jump he appeared to be tumbling end over end, and those watching would have been forgiven for fearing the worst. Three minutes in, after righting that wobble, Baumgartner declared over the radio: “My face mask is fogging up! Repeat. My facemask is fogging up!”

He then decided to open the parachute slightly earlier than planned, a precautionary move which helped him return safe and sound, but may also have prevented him from breaking the world record for “longest freefall.”

But it all added to the sense of drama. And despite the wrinkle, the world’s most famous daredevil has few regrets. “I think 20 tons have fallen from my shoulders,” was how he described his state of mind in his first post-landing interview.

“I prepared for this for seven years,” he added, according to a translation from the original German. “Even on a day like this when you start so well, there can be a little glitch, and you think you’l l have to abort... What if you’ve prepared everything and it fails on a visor problem? But in the end, I finally decided to jump. And it was the right decision.”

The jump by numbers

7.1 million people watched him on YouTube

729 Speed (mph) reached during his jump

128,000: Height in feet of Baumgartner's jump – 24 miles above the Earth